That is the profile of the 102 killers in 100 rampage attacks examined by The New York Times in a computer-assisted study looking back more than 50 years and including the shootings in 1999 at Columbine High School in Littleton, Colo., and one by a World War II veteran on a residential street in Camden, N.J., in 1949. Four hundred twenty-five people were killed and 510 people were injured in the attacks. The database, which primarily focused on cases in the last decade, is believed to be the largest ever compiled on this phenomenon in the United States.

Though the attacks are rare when compared with other American murders, they have provoked an intense national discussion about crime, education and American culture. The Times found, however, that the debate may have largely overlooked a critical issue: At least half of the killers showed signs of serious mental health problems.

The debate was most intense last year, which began with echoes of gunfire in a Salt Lake City television station in January and ended with seven Honolulu office workers dead in November. In between there was a berserk rampage by an Atlanta day trader that left 12 dead and 13 injured. A self-styled fascist attacked a Los Angeles day care center. Seven people died as a hymn ended in a Fort Worth church.

Probably the most shocking were the shootings by two students at Columbine High School who burst into suburban classrooms and killed 13 and wounded 23. The teenage killers were much like the adults The Times studied, but with important distinctions that may bring a better understanding to the problem. [Page 29.] As the anniversary of that crime, April 20, approaches, the questions about crime and culture will inevitably reverberate again.

The Times set out to examine as many of these killings as possible in an effort to learn what factors they and the people who carried them out shared. For while many possible causes have been cited, including violent video games, a decline in moral values and the easy availability of guns, there has been little serious study of this explosive violence.

The Times included only rampage homicides -- multiple-victim killings that were not primarily domestic or connected to a robbery or gang. Serial killers were not included, nor were those whose primary motives were political.

These are among the findings:

*While the killings have caused many people to point to the violent aspects of the culture, a closer look shows little evidence that video games, movies or television encouraged many of the attacks. In only 6 of the 100 cases did the killers have a known interest in violent video games. Seven other killers showed an interest in violent movies.

*In a decade that had a sharp decrease in almost all kinds of homicides, the incidence of these rampage killings appears to have increased, according to a separate computer analysis by The Times of nearly 25 years of homicide data from the Federal Bureau of Investigation. Still, these killings remain extremely rare, much less than 1 percent of all homicides.

*Society has turned to law enforcement to resolve the rampage killings that have become almost a staple of the nightly news. There has been an increasing call for greater security in schools and in the workplace. But a closer look shows that these cases may have more to do with society's lack of knowledge of mental health issues, rather than a lack of security. In case after case, family members, teachers and mental health professionals missed or dismissed signs of deterioration.

Whether they happen in a school, in a mall, in a crowded train or in a workplace, these crimes have been characterized in a language of incomprehension -- ''senseless,'' ''random,'' ''sudden,'' ''crazy.''

By contrast, murder in the heat of domestic passion or a tavern argument, in the desperation of armed robbery or in the cold calculation of gang competition, seems to make ''sense.''

But in reviewing court records and interviewing the police, victims and sometimes the killers themselves, The Times found that these killings, too, have their own logic, and are anything but random or sudden.

The rage that boiled over into homicide was clearly building in many. Of the 100 cases reviewed by The Times, 63 involved people who made threats of violence before the event, including 54 who threatened specific violence to specific people.

Richard Farley, for example, who was fired in 1987 for harassing a female co-worker, told acquaintances he was going to kill the people who had come between him and her before storming into his former workplace, killing seven. James Calvin Brady told psychiatrists he wanted to kill people, just days before he went on a rampage in an Atlanta shopping mall in 1990.

''These are not impulsive acts,'' said J. Reid Meloy, a forensic psychologist at the University of California at San Diego. ''They are not acts of affective violence, where they drink a lot and go kill someone. There's a planning and purpose, and an emotional detachment that's very long-term.''

Yet there was often a precipitating event in addition to histories of failure and mental illness -- a spark that set off the tinder, and gave the crime the appearance of being at the same time deliberate and impulsive.

''You can see someone who is morbidly depressed for a long time, and they have a suicide plan in place, but the timing is determined by impulse,'' said Kay Redfield Jamison, a professor of psychiatry at Johns Hopkins School of Medicine and author of ''Night Falls Fast: Understanding Suicide'' (Knopf, 1999).

By far the most common precipitator was the loss of a job, which was mentioned as a potential precipitator in 47 cases. A romantic issue -- a divorce or breakup -- was present in 22 cases.

''Some men see the loss of a job, or the loss of a mate, as irrevocable and catastrophic, something they can't get back or attain again,'' said David Buss, author of ''The Dangerous Passion: Why Jealousy Is as Necessary as Love and Sex'' (Free Press, 2000) and a professor of psychology at the University of Texas at Austin. ''They set out on a course to inflict the maximum cost on their rivals, even sometimes killing the woman.''

An analysis of the database found several recurring elements in rampage killings, including some that surprised the experts.

Perhaps the aspect that most set these crimes apart, aside from their spectacular nature, was this: Regular criminals try to get away with their crimes. More than a third of regular homicides went unsolved in 1997. But among the 102 killers in the Times database, not one got away. Eighty-nine never even left the scene of the crime.

In 1995, for example, after he killed three people at the Ohio trucking company where he had worked, Gerald Lee Clemons walked to the parking lot and leaned against his car calmly until the police arrived.

In 1997, Michael Carneal, a 14-year-old, killed three and wounded five at a school in Louisville, Ky. Then he laid down his gun and said, ''I'm sorry.''

More tellingly, 33 of the offenders killed themselves after their crimes. Nine tried or wanted to commit suicide, and four killed themselves later. Nine were killed by the police or others, perhaps committing what some refer to as ''suicide by cop.''

''The number of people knowingly getting killed is striking,'' Prof. Alfred Blumstein of the Heinz School of Public Policy and Management at Carnegie Mellon University said after examining the review. Professor Blumstein is the director of the National Consortium on Violence Research.

Dr. Jamison said: ''The link between suicide and homicide is a very real one, and it hasn't been studied nearly enough. It has always struck me about Columbine, people forget they committed suicide. And that's understandable -- it was the least important thing from the public point of view.''

Anthony Barbaro, a 17-year-old Regents scholar in upstate Olean, N.Y., offered a glimpse into this suicidal impulse in the note he left before he hanged himself with a knotted bedsheet in the county jail. He was awaiting trial after firing random shots out the window from the third floor of his high school, killing two passers-by and a school custodian, and wounding nine others.

''I guess I just wanted to kill the person I hate most -- myself,'' he wrote. ''I just didn't have the courage. I wanted to die, but I couldn't do it, so I had to get someone to do it for me. It didn't work out.''

One of the most remarkable insights to emerge from the survey is how much these killers differ from the typical American murderer.

Half of all murderers in this country are black. Eighty percent went to high school, and no further. Most of them killed someone they knew, or while committing another crime, like a robbery.

The rampage killers, on the other hand, were white, by far, though 18 of the 102 were black, and 7 Asian. The racial profile of the rampage killers is close to that of the entire population.

The rampage killers were overwhelmingly male -- but not entirely. Six were female, and they exhibited many of the same disturbed, aggressive characteristics of the males. Here again, however, was a distinction from regular murderers, who are about twice as likely as rampage killers to be women.

The rampage killers were far more likely to have a military background, and to kill strangers. There are intriguing age differences as well. The rampage killers were older than regular murderers, with more in their 40's and 50's and fewer in their 20's, compared with the typical killer.

Of the rampage killers who were over 25, a third had college degrees. Another third had some college education. Only nine had less than a high school diploma.

And there seemed to be no urban bias for these crimes, as there is for other violent crimes; 31 were in suburban areas, 25 were in small towns or rural areas. Forty two of those surveyed committed their crimes in urban areas.

That profile -- a group that is largely suicidal, and shows few of the demographic patterns of poverty and race associated with regular crime -- suggests that mental illness plays a huge role, psychiatrists say.

''Mental illness does not vary in different races, but socioeconomics do,'' said Dr. Lothar Adler, director of a psychiatric hospital in Muhlhausen, Germany, and author of ''Amok,'' a book on multiple murder.

The Times found much evidence of mental illness in its subjects. More than half had histories of serious mental health problems -- either a hospitalization, a prescription for psychiatric drugs, a suicide attempt or evidence of psychosis.

Of the 24 who had been prescribed psychiatric drugs, 14 had stopped taking them when they committed their crimes. Mr. Clemons, for instance, ran out of drugs a week before his crime, according to relatives.

Recent studies have shown that the mentally ill are no more violent than other people, except when they are off their medications, or have been abusing drugs or alcohol.

Indications of mental illness were far more common among the 100 cases than was evidence supporting popular explanations that emerged in the days after some of these spectacular events. Violent video games or television were mentioned in only a handful of cases. Three killers showed an interest in the occult. Racist ideas were apparent in the backgrounds of 16.

But 48 killers had some kind of formal diagnosis, often schizophrenia. Some of the diagnoses came after examinations by psychiatrists in trial preparations -- which did not usually help in their defense, as only eight avoided conviction on grounds of insanity. Twenty-five killers received diagnoses before their crimes, which illustrates another recurring issue: They do not just suddenly snap. Many have long histories not only of mental illness but of failure and dislocation.

In spite of their education levels, for instance, a striking number -- more than half -- were unemployed.

''The high education level is one thing I hadn't anticipated, and the link to unemployment is another thing I didn't realize,'' Professor Blumstein said. ''One of the things that education does is raise expectations, and raised ones are more readily frustrated.''

For people without the emotional resources to accommodate it, frustration ''can lead to rage, can lead to suicide,'' Professor Blumstein said.

These crimes are not new. Public rampage killings first entered the national consciousness with Charles Whitman, who stood on the University of Texas's tower in 1966, firing his rifle at students, killing 14 people.

Nor are they peculiarly American. The best scientific thinking, in a field that is admittedly understudied, now holds that multiple, public murder occurs at a fairly constant level across time and cultures. What some people call ''running amok,'' a term first used in Malaysia to describe frenzied, indiscriminate killing, has been observed in many cultures, with weapons as varied as grenades and tanks in addition to high-powered handguns.

''Even though homicide rates and suicide rates are very different from country to country,'' said Peter M. Marzuk, a professor in the department of psychiatry at the Weill Medical College of Cornell University, ''the rates of murder-suicide are really the same throughout the world.''

Yet there is a strong impression that they have become more common. In an effort to confirm the trend, The Times analyzed F.B.I. reports of all homicides since 1976. Each year there were 15,000 to 22,000 homicides, but very few involved three or more victims.

That universe shrank even more, to just a few dozen, when The Times weeded out those involving robbery or gang violence, and those in which the primary victim was a family member.

What is left is the closest thing there is to a census of rampage killings -- about one-tenth of one percent of all killings.

And it shows that in the 1990's, they increased.

Their number remained fairly consistent from 1976 to 1989, averaging about 23 a year, only once going above 30. But between 1990 and 1997, the last year for which data was available, the number averaged over 34, dipping below 30 only once, in 1994.

''In the early 90's, for some reason, it increased, and seems to have a different level since,'' said Steven Messner, a criminologist at the State University of New York at Albany, who reviewed the numbers at the request of The Times.

There are many possible explanations. But the shift coincides, roughly at least, with a trend of increasing availability of more lethal weapons. In the late 1980's, the production of semiautomatic pistols in the United States overtook the production of revolvers, and with their larger ammunition magazines and faster reloading, semiautomatics have added to the potential for mayhem.

The effect may be apparent in the number of deaths per murderous incident, which suddenly increased in 1993 and has remained high since, according to the analysis of F.B.I. data by The Times.

''You have drastically increased the ability to inflict death and injury,'' said Tom Diaz, author of ''Making a Killing: The Business of Guns in America'' (New Press, 1999) and a senior policy analyst at the Violence Policy Center. ''That means you can shoot more rounds faster and easier, what they call spray and pray.''

In the Times study, wielders of semiautomatics inflicted more injuries. The ratio of maimed to killed victims was 50 percent higher than for those who used other weapons. Yet, the increased availability of high-powered weapons may not explain everything. Some kinds of multiple murder have declined or remained static. Killings of three or more people to cover up another felony, like robbery, have not increased, for example. Neither have multiple killings of relatives. The number of incidents in which three or more died and the principal victim was a family member has remained fairly steady, around 30 cases a year.

''It used to be the most common type of this violence was in the family,'' said James Alan Fox, author of ''Overkill: Mass Murder and Serial Killing Exposed'' (Dell, 1996) and one of the nation's foremost experts on mass murder. ''Now it's no longer true. It's in the workplace and in the schools.''

Experts believe the crimes may be feeding on each other, particularly in an era of saturation coverage by cable television. Fourteen of the killers expressed knowledge about their predecessors.

For example, Ladislav Antalik, a Czech immigrant who killed two former co-workers and then himself after being fired from his job in Research Triangle Park, N.C., in 1994, had a newspaper article in his car describing a previous massacre.

The Columbine killers talked of doing it bigger and better than it had been done before. William Kreutzer, known as Crazy Kreutzer, as he set out to mow down a company of soldiers at Fort Bragg with an assault rifle and a semiautomatic pistol, told a friend he knew what the record number of multiple killings was.

But beyond the question of whether one event triggered the next, experts say the recent increases in these crimes strongly suggest a social contagion.

''Why do you get a lot of people doing the same thing?'' said Joseph Westermeyer, a psychiatrist at the University of Minnesota who has studied epidemics of explosive murder in other cultures. ''I think there is this copycat element.''

Dr. Adler, in his book, documented two cases of soldiers running amok with a tank in Germany in the 1980's after a widely publicized tank attack there. Army security was increased, and ''tank amok never happened in Germany again,'' Dr. Adler said.

An angry, depressed, unstable, perhaps mentally ill person picks up a gun because it has become a known alternative. ''Something that was inconceivable to many people suddenly becomes conceivable,'' Dr. Messner said.

''The transmission mechanism seems to be nothing more or less than that it's an idea that's in the air,'' said Philip Cook, a professor of public policy at Duke University, who has studied social contagions. ''So you have these kind of catastrophic consequences from what seems a minor change in the environment.''

How the Study Was Conducted

The New York Times set out to study rampage killings by assembling a detailed database of as many such crimes as could be discovered by searching news clippings in all 50 states, scientific papers and other sources.

Times researchers and reporters found 100 cases that met strictly defined criteria aimed at encompassing the kind of crimes that seem to have become more common recently. The crimes had to have had multiple victims, at least one of whom died, and to have occurred substantially at one time and in a place where people gather -- a workplace, a school, a mall, a restaurant, a train. Multiple killings that were a result of domestic strife, robbery or political terrorism were excluded, as were serial killings.

Reporters and researchers reviewed newspaper articles and court transcripts, and interviewed prosecutors, victims, families and, when possible, the killers. Reporters recorded into a database more than 90 separate pieces of information on each crime, including age, mental health histories, victim relationships, weapons used, warning signs, location, time of day and criminal records.

Ford Fessenden, a database reporter at The Times, coordinated the research.

The 100 cases include 20 shootings at schools, 11 at restaurants or shopping malls and 32 at the killer's workplace. There were 102 killers. Four hundred twenty five people were killed and 510 injured.

In some cases, it was difficult to get precise information, as news accounts and even police reports varied. And while extensive efforts were made to be as complete as possible, there is no central list of multiple murders, and the database does not include every attack of this type over the last 50 years.

Still, the experts acknowledged it to be the largest and most detailed database devoted exclusively to such murders in the United States, and suggested it should be considered an initial step in a systematic study of a largely unexamined field.

''This should be seen as a way of starting the conversation and getting good social science going,'' said Franklin Zimring, director of the Earl Warren Legal Institute at the University of California at Berkeley.

''It's not science and shouldn't be addressed as science,'' said Alfred Blumstein, director of the National Consortium on Violence Research, who was shown The Times's findings. ''But I think it's aggressive and careful.''

Correction: April 11, 2000, Tuesday An article on Sunday about rampage killings in the United States misidentified the Kentucky city where Michael Carneal killed three people at a school in 1997. It was West Paducah, not Louisville. A map with the article misplaced the symbol for the outbreak in which Sylvia Seegrist killed three people in 1985. It occurred in Pennsylvania, not Illinois.

Reporting for this series was by Fox Butterfield, Ford Fessenden, William Glaberson and Laurie Goodstein, with research assistance from Anthony Zirilli and other members of the news research staff of The New York Times.